{"id":"https://openalex.org/W2142094679","doi":"https://doi.org/10.1142/s0218127411030593","title":"CHAOTIFICATION OF NONAUTONOMOUS DISCRETE DYNAMICAL SYSTEMS","display_name":"CHAOTIFICATION OF NONAUTONOMOUS DISCRETE DYNAMICAL SYSTEMS","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W2142094679","doi":"https://doi.org/10.1142/s0218127411030593","mag":"2142094679"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411030593","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411030593","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110370998","display_name":"Qiuling Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"QIULING HUANG","raw_affiliation_strings":["Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China","Department of Statistics and Mathematics, Shandong Economic University, Jinan, Shandong 250101, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China","institution_ids":["https://openalex.org/I154099455"]},{"raw_affiliation_string":"Department of Statistics and Mathematics, Shandong Economic University, Jinan, Shandong 250101, P. R. China","institution_ids":["https://openalex.org/I59483232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101948113","display_name":"Yuming Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YUMING SHI","raw_affiliation_strings":["Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":null,"display_name":"LIJUAN ZHANG","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"LIJUAN ZHANG","raw_affiliation_strings":["Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shandong University, Jinan, Shandong 250100, P. R. China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110370998"],"corresponding_institution_ids":["https://openalex.org/I154099455","https://openalex.org/I59483232"],"apc_list":null,"apc_paid":null,"fwci":0.2409,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.59822021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"21","issue":"11","first_page":"3359","last_page":"3371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sawtooth-wave","display_name":"Sawtooth wave","score":0.8337694406509399},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6237231492996216},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5658648610115051},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5492879152297974},{"id":"https://openalex.org/keywords/feedback-control","display_name":"Feedback control","score":0.5027968883514404},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5027503967285156},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5001826286315918},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.495961993932724},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48320329189300537},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4102838635444641},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.406521201133728},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.37741583585739136},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37118804454803467},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09643223881721497},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09592685103416443}],"concepts":[{"id":"https://openalex.org/C148837635","wikidata":"https://www.wikidata.org/wiki/Q1742397","display_name":"Sawtooth wave","level":2,"score":0.8337694406509399},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6237231492996216},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5658648610115051},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5492879152297974},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.5027968883514404},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5027503967285156},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5001826286315918},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.495961993932724},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48320329189300537},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4102838635444641},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.406521201133728},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37741583585739136},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37118804454803467},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09643223881721497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09592685103416443},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127411030593","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411030593","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1496745782","https://openalex.org/W1569683457","https://openalex.org/W1598317411","https://openalex.org/W1944192336","https://openalex.org/W1970135831","https://openalex.org/W1973822038","https://openalex.org/W1985039283","https://openalex.org/W1995837155","https://openalex.org/W1995945562","https://openalex.org/W1998538686","https://openalex.org/W2002681938","https://openalex.org/W2024026135","https://openalex.org/W2028985073","https://openalex.org/W2040112596","https://openalex.org/W2042083138","https://openalex.org/W2046529028","https://openalex.org/W2055660413","https://openalex.org/W2061152410","https://openalex.org/W2067904577","https://openalex.org/W2137162754","https://openalex.org/W2139153229","https://openalex.org/W2142887069","https://openalex.org/W2153903365","https://openalex.org/W2166393890","https://openalex.org/W2574026466","https://openalex.org/W4248796009","https://openalex.org/W4252910012","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W2230606337","https://openalex.org/W4250831671","https://openalex.org/W2089869689","https://openalex.org/W4388681848","https://openalex.org/W2078952919","https://openalex.org/W2945666329","https://openalex.org/W2617651062","https://openalex.org/W2377513064","https://openalex.org/W2016990342","https://openalex.org/W2952544653"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3],"the":[4,34,47],"chaotification":[5,22],"of":[6,50],"nonautonomous":[7],"discrete":[8],"dynamical":[9],"systems":[10,40],"in":[11,46],"finite-dimensional":[12],"and":[13,27],"general":[14,25],"Banach":[15],"spaces":[16],"by":[17],"feedback":[18],"control":[19],"techniques.":[20],"Several":[21],"schemes":[23],"with":[24],"controllers":[26,35],"sawtooth":[28],"function":[29],"are":[30,36,41],"established,":[31],"respectively,":[32],"where":[33],"time-invariant.":[37],"The":[38],"controlled":[39],"proved":[42],"to":[43],"be":[44],"chaotic":[45],"strong":[48],"sense":[49],"Li\u2013Yorke.":[51]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}